greyhound vs hound dog

greyhound and hound dog both are nouns.

Word	Noun	Adjective	Verb	Adverb
greyhound	Yes	No	No	No
hound dog	Yes	No	No	No

As nouns, hound dog is a hypernym of greyhound; that is, hound dog is a word with a broader meaning than greyhound:

greyhound: a tall slender dog of an ancient breed noted for swiftness and keen sight; used as a racing dog
hound dog: any of several breeds of dog used for hunting typically having large drooping ears

Other hypernyms of greyhound include hound, racer.

greyhound (noun)	hound dog (noun)
a tall slender dog of an ancient breed noted for swiftness and keen sight; used as a racing dog	any of several breeds of dog used for hunting typically having large drooping ears